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Fixation in bisexual models with variable population sizes

Published online by Cambridge University Press:  14 July 2016

M. Möhle
M. Möhle*
Affiliation:
University of Chicago
*
∗Postal address: The University of Chicago, Department of Statistics, 5734 University Avenue, Chicago, Illinois 60637, USA. Also at Johannes Gutenberg-Universität Mainz, Fachbereich 17 Mathematik, Saarstraβe 21, 55099 Mainz, Germany.
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Abstract

A general exchangeable bisexual model with variable population sizes is introduced. First the forward process, i.e. the number of certain descending pairs, is studied. For the bisexual Wright-Fisher model fixation of the descendants occurs, i.e. their proportion tends to 0 or 1 almost surely.

The main part of this article deals with necessary and sufficient conditions for ultimate homozygosity, i.e. the proportion of an arbitrarily chosen allelic type tends to 0 or 1 almost surely. The results are applied to a bisexual Wright-Fisher model and to a bisexual Moran model.

Keywords

EXCHANGEABLE PROCESSESFIXATIONHOMOZYGOSITYMORAN MODELWRIGHT-FISHER MODEL

MSC classification

Primary: 92D25: Population dynamics (general)
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 436 - 448
Copyright
Copyright © Applied Probability Trust 1997 

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References

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